Using the Jones Polynomial to Prove Infinite Families of Knots Satisfy the Cosmetic Surgery Conjecture

F. M. Brady

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arXiv · 2512.20511

Using the Jones Polynomial to Prove Infinite Families of Knots Satisfy the Cosmetic Surgery Conjecture

F. M. Brady

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Abstract

This paper computes the Jones polynomial and the invariants obstructing cosmetic surgery which are derived from it for two infinite families of knots, proving they satisfy the Purely Cosmetic Surgery Conjecture. Both the method of computation and the method for generating families of knots extend.

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F. M. Brady. 2025-12-23. Using the Jones Polynomial to Prove Infinite Families of Knots Satisfy the Cosmetic Surgery Conjecture. https://arxiv.org/abs/2512.20511

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